The Crew threatened first when Federico Higuain threaded a through-ball into the path of Kamara, but his strike went just wide of the post from inside the box.
Johnson made another fine stop to deny the Crew when he displayed quick reactions to save Kamara's effort from close range.
Columbus finally took the lead in the 41st minute when Finlay lifted a cross into the box from the right and Kamara powered a header past Johnson.
The Fire came close again when David Accam pounced on a loose ball inside the area, but his strike was well stopped by Clark.
In the dying minutes, Jason Johnson had the chance to net an equaliser as he latched on to a cross into the box, but put his header wide of the target.